There is no "technically" about it. Mozart wasn't Austrian. Being Austrian is and was being a citizen of Austria. Mozart was not a citizen of Austria, ergo he was not Austrian. However, Mozart was born and lived most of his life in what is today Austria in a city with very close cultural ties to what is modern Austria but Saltzburg did not become part of Austria until 1805. In Mozarts day an Austrian was a person of the Archduchy of Austria, again, Mozart was not.

EDIT: It is worth mentioning that the strong national identities we today asociate with citizenship of a certain nation are relatively recent inventions. National identities in Mozart's day were more closely tied to socio-cultural groups in which case Mozart, in his day, considered himself German (but again, this was not as such a reference to being a German national in modern terms but rather a reference to modern day Germany, Austria and Saltzburg all being within the German socio-cultural sphere).

Bonus Answer: Yes, until he was granted American citizenship in 1891 Tesla was an Austrian citizen by birth.